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Volume 6, Issue 4
Fast Parallel Algorithms for Computing Generalized Inverses $A^+$ and $A_{MN}^+$

Guo-Rong Wang & Sen-Quan Lu

J. Comp. Math., 6 (1988), pp. 348-354.

Published online: 1988-06

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  • Abstract

The parallel arithmetic complexities for computing generalized inverse $A^+$, computing the minimum-norm least-squares solution of $Ax=b$, computing order $m+n-r$ determinants and finding the characteristic polynomials of order $m+n-r$ matrices are shown to have the same grawth rate. Algorithms are given that compute $A^+$ and $A_{MN}^+$ in $O(\log r\dot \log n+\log m)$ and $O(\log^2n+\log m)$ steps using a number of processors which is a polynomial in $m, \ n$ and $r$ $(A\in B_r^{m\times n},r=rank \ A)$.

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@Article{JCM-6-348, author = {Wang , Guo-Rong and Lu , Sen-Quan}, title = {Fast Parallel Algorithms for Computing Generalized Inverses $A^+$ and $A_{MN}^+$}, journal = {Journal of Computational Mathematics}, year = {1988}, volume = {6}, number = {4}, pages = {348--354}, abstract = {

The parallel arithmetic complexities for computing generalized inverse $A^+$, computing the minimum-norm least-squares solution of $Ax=b$, computing order $m+n-r$ determinants and finding the characteristic polynomials of order $m+n-r$ matrices are shown to have the same grawth rate. Algorithms are given that compute $A^+$ and $A_{MN}^+$ in $O(\log r\dot \log n+\log m)$ and $O(\log^2n+\log m)$ steps using a number of processors which is a polynomial in $m, \ n$ and $r$ $(A\in B_r^{m\times n},r=rank \ A)$.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9523.html} }
TY - JOUR T1 - Fast Parallel Algorithms for Computing Generalized Inverses $A^+$ and $A_{MN}^+$ AU - Wang , Guo-Rong AU - Lu , Sen-Quan JO - Journal of Computational Mathematics VL - 4 SP - 348 EP - 354 PY - 1988 DA - 1988/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9523.html KW - AB -

The parallel arithmetic complexities for computing generalized inverse $A^+$, computing the minimum-norm least-squares solution of $Ax=b$, computing order $m+n-r$ determinants and finding the characteristic polynomials of order $m+n-r$ matrices are shown to have the same grawth rate. Algorithms are given that compute $A^+$ and $A_{MN}^+$ in $O(\log r\dot \log n+\log m)$ and $O(\log^2n+\log m)$ steps using a number of processors which is a polynomial in $m, \ n$ and $r$ $(A\in B_r^{m\times n},r=rank \ A)$.

Wang , Guo-Rong and Lu , Sen-Quan. (1988). Fast Parallel Algorithms for Computing Generalized Inverses $A^+$ and $A_{MN}^+$. Journal of Computational Mathematics. 6 (4). 348-354. doi:
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